8 papers
Reversion Porisms in Conics
Lorenz Halbeisen, Norbert Hungerbühler, Marco Schiltknecht
We give a projective proof of the butterfly porism for cyclic quadrilaterals and present a general reversion porism for polygons with an arbitrary number of vertices on a conic. We…
Lights Out on graphs
Abraham Berman, Franziska Borer, Norbert Hungerbühler
We model the Lights Out game on general simple graphs in the framework of linear algebra over the field . Based upon a version of the Fredholm alternative, we introduc…
Exotic Steiner Chains in Miquelian Möbius Planes
Norbert Hungerbühler, Gideon Villiger
In the Euclidean plane, two intersecting circles or two circles which are tangent to each other clearly do not carry a finite Steiner chain. However, in this paper we will show tha…
Congruent number elliptic curves with rank at least two
Lorenz Halbeisen, Norbert Hungerbühler
We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of .
Communicating harmonic pencils of lines
Norbert Hungerbühler, Clemens Pohle
Suppose there are harmonic pencils of lines given in the plane. We are interested in the question whether certain triples of these lines are concurrent or if triples of interse…
Resistors in dual networks
Martina Furrer, Norbert Hungerbühler, Simon Jantschgi
Let be a finite plane multigraph and its dual. Each edge of is interpreted as a resistor of resistance , and the dual edge is assigned the dual resistanc…